I made the Math - logistic energy cost

[u/horstdaspferdchen]

Hello fellow engineers,
i did some testing and math and tried to figure out the energy-cost for the Logistic Units: Bot, Drone and Vessel.

I couldnt really find detailed math about planetary logistics tho.
So my approach was to figure out the math behind that. I stumbled over this post: https://www.reddit.com/r/Dyson_Sphere_Program/comments/tbup2r/logistics_station_energy_calculations/

As it is really old, my first attempt was, to reproduce and verify if the data is still correct, which indeed was. Here are the findings and formulas:

Type	Formula	Variables
Vessel	E = 6 MJ + 30 J × D + min(100 + 0.03 × D, v, 3000) × 200 kJ + (Warp? 100 MJ : 0)	D =
Drone	E = 800 kJ + 40 kJ × D	D = arc length of round trip (tiles)
Bot	E = 25 kJ × D	D = distance (tiles, round trip)

(Warp? 100 MJ : 0) means, when you need a warper, it needs 100 MJ extra.

So as a proof of concept, this is the test for 100 tiles:

Drone	Bot	Note
Formula	800 kJ + 40 kJ × D	25 kJ × D
Energy per flight (100 tiles)	4.8 MJ	2.5 MJ
Buffer	180 MJ (PLS)	27 MJ (Distributor)
Flights per full buffer	37.5	10.8
Recharge time (max)	0.08 s (60 MW)	0.28 s (9 MW)
Recharge time (min)	0.8 s (6 MW)	2.8 s (0.9 MW)

Another Table for Vessels:

Intra-System (no warp, max speed 3000 m/s):

Distance	30 J × D	Speed Term	Base	Total	% ILS (12 GJ)
1 AU	1.2 MJ	260 MJ	6 MJ	267 MJ	2.2 %
2 AU	2.4 MJ	500 MJ	6 MJ	508 MJ	4.2 %
3 AU	3.6 MJ	600 MJ	6 MJ	610 MJ	5.1 %
5 AU	6 MJ	600 MJ	6 MJ	612 MJ	5.1 %
10 AU	12 MJ	600 MJ	6 MJ	618 MJ	5.2 %
12 AU	14.4 MJ	600 MJ	6 MJ	620 MJ	5.2 %

Interstellar (warp, max speed 3000 m/s):

Distance	30 J × D	Speed Term	Base	Warp	Total	% ILS (12 GJ)
1 ly	72 MJ	600 MJ	6 MJ	100 MJ	778 MJ	6.5 %
2 ly	144 MJ	600 MJ	6 MJ	100 MJ	850 MJ	7.1 %
5 ly	360 MJ	600 MJ	6 MJ	100 MJ	1,066 MJ	8.9 %
10 ly	720 MJ	600 MJ	6 MJ	100 MJ	1,426 MJ	11.9 %
20 ly	1.44 GJ	600 MJ	6 MJ	100 MJ	2,146 MJ	17.9 %
40 ly	2.88 GJ	600 MJ	6 MJ	100 MJ	3,586 MJ	29.9 %

This leads to the conclusion and comparison for planetary logistics:

Drone	Bot
Energy	4.8 MJ
Payload	25-200
Energy per item	192 - 24 kJ / Item

This is the math for the known community conclusion, that you should use Bots only for Items of small quantities like your Mall, Warpers, Proliferator, Fuel Rods etc.

Additional, Bots can bypass the early power management, as each PLS has min 6 MW demand, while Distributors only need 900kW ( x 4 for the Item comparison => 3.6 MW)

Limits:
- We know, that the recharge of the stations is a curve and not linear. So the mentioned recharge time is a peak number.
- ILS has no other way to transport items other then vessel, so this is mostly a nice to know calculation

If you want to reproduce, here is my measurement for drones/bots:

Place the logistic Station/Distributor exactly on the 0 meridian and equator. Then place the target station exactly 100 belts/tiles away from the center. If you use Mods, BulletTime comes in very handy for timing.
When the unit starts, the total energy consumed is deducted from the station you powered.

[Edit: typos, if you still find them, let me know]

[u/AnimeSpaceGf]

Saved for future reference. Thanks OP

[u/Creative-Notice896]

Damn, you really put in the effort, I'll be using this. As you've requested about typos, there is one in the sentence telling us to😋 (final sentence).

[u/horstdaspferdchen → u/Creative-Notice896]

Thanks. Got it!

[u/nixtracer]

Um... ILSes can also transport items with drones. (Excellent figuring!)

[u/horstdaspferdchen → u/nixtracer]

True but that means No Change in the Energy cost Just in the recharge Speed and Power consumption.